You can use our live shipping rate modification snippet to hide the rates you don't want to see based upon weight and/or price (among other criteria). This article gives step-by-step instructions for installation, but does require familiarity with JavaScript in order to create the logic needed for your particular situation: https://wiki.foxycart.com/v/2.0/snippets/live_rate_shipping_modification

If you aren't familiar with JavaScript, you can reach out to help@foxycart and let us know precisely which rates to show for what weights and/or pricing and we can help you out from there (you can also do it by product, if desired).